When using Dyntopo, is there a way to adjust how far each vertex is pushed or pulled?
You can press Shift+F to adjust the strength of the brush you are currently using. 

You can also adjust the detail size with Shift+D 
(This will display as a percentage or as a pixel count depending on the detail type being used.) The manual has an  explanation of each one.

Changing the radius of the brush with F as needed is also useful.